Testing for Identication in GMM under Conditional Moment Restrictions

This paper proposes a simple test for global identi…cation of Generalized Method of Moments (GMM) estimators in models de…ned by conditional moment restrictions. The test is based on comparing two estimators, one which is always consistent, even under global identi…cation failure of the unconditional model, and the GMM estimator. It is shown that the test is able to detect Pitman alternatives, including the popular ones in the weak identi…cation and/or weak instruments literature. A Monte Carlo experiment shows that the new test has excellent size and power properties already for moderate sample sizes. In an empirical application we study the identi…cation power of GMM for some asset pricing models. Key words and phrases: Conditional moment restrictions; Generalized Method of Moments; Global Identi…cation; Asset Pricing. JEL Classi…cation Number: C12; C13; C32. 1Department of Economics, The University of York. 2Department of Economics, Indiana University, email: [email protected]. Research funded by the Spanish Plan Nacional de I+D+I, reference number SEJ2007-62908. I thank Lin Zhu for excellent research assistance. 3Department of Economics, Yale University.